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2018 Local homology, Koszul homology and Serre classes
Kamran Divaani-Aazar, Hossein Faridian, Massoud Tousi
Rocky Mountain J. Math. 48(6): 1841-1869 (2018). DOI: 10.1216/RMJ-2018-48-6-1841

Abstract

Given a Serre class $\mathcal {S}$ of modules, we compare the containment of Koszul homology, Ext modules, Tor modules, local homology and local cohomology in $\mathcal {S}$ up to a given bound $s \geq 0$. As applications, we give a full characterization of Noetherian local homology modules. Furthermore, we establish a comprehensive vanishing result which readily leads to formerly known descriptions of the numerical invariants' width and depth in terms of Koszul homology, local homology and local cohomology. In addition, we recover a few renowned vanishing criteria scattered throughout the literature.

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Kamran Divaani-Aazar. Hossein Faridian. Massoud Tousi. "Local homology, Koszul homology and Serre classes." Rocky Mountain J. Math. 48 (6) 1841 - 1869, 2018. https://doi.org/10.1216/RMJ-2018-48-6-1841

Information

Published: 2018
First available in Project Euclid: 24 November 2018

zbMATH: 06987228
MathSciNet: MR3879305
Digital Object Identifier: 10.1216/RMJ-2018-48-6-1841

Subjects:
Primary: 13C05, 13D07, 13D45

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

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Vol.48 • No. 6 • 2018
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